Inconsistent Toggles in Windows 10 Taskbar Menu

There’s something I found really odd about the Windows 10 taskbar. There are two special buttons next to the Start button: the Search button, and the Task View button. You can toggle the visibility of each from the context menu that comes up when you right click on the taskbar.

We can toggle the Task View button by simply clicking on the “Show Task View button” item in the menu. When the Task View button is visible, this item is checked:

…and when it’s not visible, the item is not checked:

Simple, no? Let’s do the same for the Search button. Right now it’s on…

So when I click “Show search icon”, following the same logic as with the Task View button, I would expect it to disappear, right?

Nope. Clicking that won’t do anything, because you instead have to select “Hidden”. Then, when Search is not visible, it looks like this instead:

Okay, it’s easy to get used to this after tripping on it the first time. But why would anyone ever provide these kinds of confusing and inconsistent options?

Aside from this, that Search submenu is clearly overkill, given that they could have implemented a single toggle menu item as with Task View. This is exactly like using two checkboxes for the opposites of same thing and expecting them to be mutually exclusive. By way of analogy, can you imagine how stupid this would look?

This would tell you that the Male and Female options are unrelated; you could potentially pick both.

Update 24th December 2015: As pointed out in these comments on Reddit, apparently the reason for having a separate menu for the Search icon is that in regions where Cortana is enabled, there are actually three options. They could have at least used bullets instead of checkmarks though, which would have made them feel like radio buttons (making the mutual exclusion obvious) rather than checkboxes.